In a large mixing bowl, combine one cup of softened unsalted butter and two cups of confectioners' sugar. Beat until light and fluffy, about 2-3 minutes.

Stir in two teaspoons of peppermint extract and mix on low speed until evenly incorporated, about 30 seconds.

Sift together two cups of all-purpose flour, three tablespoons of cornstarch, and a pinch of salt in a separate bowl. Gradually add to the butter mixture until a soft dough forms.

Roll the dough into small balls, about one inch in diameter, and place them on a baking sheet lined with parchment paper. Flatten each ball slightly.

Refrigerate the shaped cookies for approximately 30 minutes, or until firm to the touch.

Prepare the frosting by creaming together half a cup of softened butter, two cups of confectioners' sugar, two tablespoons of milk, and one teaspoon of peppermint extract. Beat until smooth and fluffy.

Frost each cookie generously using a knife or spatula. Consider using a piping bag for decorative swirls.

Sprinkle crushed peppermint candies on top of each frosted cookie and allow them to set at room temperature for about 30 minutes.